Molecular simulations of small gas diffusion and solubility in copolymers of styrene
Introduction
The research on diffusion, sorption and permeation of small molecules in polymeric materials has always been fundamental, since there are many industrially important processes that utilize polymeric materials as membranes or barriers, such as food packaging, gas separation and encapsulation of electronic components [1], [2]. In the last decade, it has become possible to establish structure–property relationships by means of molecular simulations [3], which would aid the design and material selection for the applications mentioned above.
Molecular dynamics (MD) simulation is an approach, which is effective for the investigation of the equilibrium and dynamic properties of polymeric microstructures. MD has been extensively used over the last 10 years in order to examine the diffusion mechanism of small gas molecules in polymers. The diffusion mechanisms of small molecules in polymer structures of poly(ethylene) [4], [9], poly(propylene) [5], [6], poly(isobutylene) [7], [8], [9], [10], poly(dimethylsiloxane) [11], [12], [13], poly(butadiene) [14], poly(styrene) [15], poly(imide) and poly(amide imide) [16], [17], poly(vinyl alcohol) membranes [18], poly(vinyl alcohol) hydrogels [19], poly(benzoxazine) [20], poly(2,6-dimethyl-1,4-phenylene oxide) [21], poly[1-(trimethylsilyl)-1-propyne] [22], poly(organophosphazenes) and poly(dibutoxyphosphazenes) [23], poly(ether-ether-ketone) [24] have already been investigated.
Transition-state approach (TSA) [25], [26] is an alternative, efficient method that is commonly used to predict the diffusion coefficients and the solubility values, based on the transition-state theory. TSA is especially effective for polymeric systems with lower permeability coefficients, where MD simulations would not produce statistically reliable results due to computational time limitations [27], [28], [29].
In this work, the gas transport parameters, i.e. the diffusion coefficients and solubility values, for small penetrant molecules (He, H2, N2, Ne, O2, CO2, CH4, Ar) in the amorphous structures of atactic polystyrene (PS), poly(styrene-alt-maleic anhydride) (SMA) and poly(styrene-stat-butadiene) (SBR) are determined by means of TSA. In addition, the diffusion of water is studied in these matrices using fully atomistic MD simulations, which provide insight about the local structural relaxation and the free volume distributions of the matrices. Moreover, the specific interactions of the water molecules among themselves and with the matrices are investigated using pair correlation functions.
PS, a commodity polymer used in packaging, domestic electrical appliances, electronic equipments, and SBR, a copolymer of styrene widely used in products ranging from rubber bands to automotive tires, have both already been well-characterized experimentally. The experimental solubility, diffusion and permeability coefficients for most of the small penetrant molecules in PS and SBR are available. Another copolymer of styrene, SMA, used in auto parts and appliances, has been an active topic of research during recent years. To our knowledge, there have been no fully atomistic MD or TSA studies performed on SMA and SBR. Therefore our results will provide insight about the properties of SMA and SBR at the molecular level. There are several MD simulations performed on the PS matrix [15], [30], [31], [32], but TSA results and the diffusion of H2O in this matrix have not been reported so far. Although the three structures have the styrene monomer in common; PS (glass transition temperature, ) and SMA are glassy, while SBR ( when the weight percentage of styrene:butadiene is 50:50) [33] is rubbery at room temperature.
We would like to quantitatively compare these matrices with the aim of pinpointing those equilibrium and/or dynamic properties that play dominant roles in determining the differences among the gas transport parameters of these matrices. TSA will be particularly useful for the estimation of the diffusion coefficients of gases in the glassy systems due to its computational efficiency, whereas MD will provide more detailed information about the equilibrium and dynamic properties of these systems. As a result, the two copolymers containing styrene, SBR and SMA, will be characterized at a molecular scale, specifically in terms of gas transport properties.
Section snippets
Construction of polymer microstructures
Bulk structures of atactic polystyrene (PS), poly(styrene-alt-maleic anhydride) (SMA) and poly(styrene-stat-butadiene), also called styrene–butadiene rubber (SBR), were generated and simulated by using the commercial software of Accelrys (Insight II-Discover) [34]. The COMPASS (Condensed-phase Optimized Molecular Potentials for Atomistic Simulation Studies) forcefield was applied in all simulations [35]. The calculations were performed on SGI O2 workstations.
Monomers and single chains. The
Evaluation of the TSA results
Table 3 lists the smearing factors calculated by the self-consistent field procedure for all types of penetrant molecules in each cell. These values fall in the same range with the smear factors used by Gusev et al. for glassy atactic polyvinylchloride and rubbery polydimethylsiloxane structures [27].
Table 4 gives the computed densities of the specific snapshots, chosen for TSA calculations. The free volume percentages and solubility parameters, δ(sim), of these cells are also listed together
Concluding remarks
Transition state approach is used to calculate the diffusion coefficients (D) and the solubility values (S) of simple gases in SMA, PS and SBR matrices, and also predict the permeability coefficient (P) as the product of D and S. As a result, gas transport parameters in these matrices are estimated with reasonable accuracy, i.e. within less than an order of magnitude of the experimental results. The permeability of these matrices to simple gases decreases in the following order: P(SBR)>P(PS)>P
Acknowledgements
This work has been supported by the Bogazici University B.A.P. (01HA501), DPT Project (01K120280), ARCELIK A.S, and the Turkish Academy of Sciences in the framework of the Young Scientist Award Program (PD-TUBA-GEBIP/2002-1-9). The authors thank Turgut and Nihan Nugay for their suggestion of the SMA matrix.
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